David Moyes says there is a "good possibility" that Sylvain Distin will follow his fellow centre-back Phil Jagielka in signing a new Everton contract.

England international Jagielka, 30, committed himself to the club on Thursday by signing a two-year contract extension that will keep him at Goodison Park until the summer of 2017.

Distin signed a one-year contract last summer, and is likely to be offered a similar deal for next season. The 35-year-old Frenchman has been one of Everton's most reliable performers since arriving from Portsmouth in the summer of 2009, and Moyes is hopeful of keeping him.

Everton's manager was delighted to get Jagielka signed up, saying: "He's been excellent since he came here. He's worked his way into the England squad, which is really important for him and for us. He deserves it because he's been very good here."

Asked about the chances of Distin following Jagielka in signing a new contract, Moyes said: "Yeah. I think that's a good possibility as well."

Everton lie fifth in the Premier League after winning four of their last six games, and are in confident mood as they prepare to travel to League Two side Cheltenham in the FA Cup on Monday for a third-round tie that will be screened live on ESPN.

But Moyes, who was at Edgar Street last month to watch Mark Yates' side set up Monday's tie with a 2-1 second-round replay win at Hereford, is wary of an upset.

Everton were dumped out in the third round by a Shrewsbury side who were bottom of the Football League in 2003, and were beaten at home by League One side Oldham at the same stage five years later.

He has happier memories of a tricky cup trip in 2009, when a third-round victory at Macclesfield, then in League Two, sparked a run to the FA Cup final.

Moyes said: "We won that one at Macclesfield, but I could go back to other ones where we've lost in the FA Cup in early rounds.

"We've seen both sides of it, so we know what it's like. We know how difficult it will be. I've worked at that level before as well, so I know how important the game will be for Cheltenham.

"I totally understand what you've got to do to get through in the FA Cup. You've got to play well, and you've got to be ready for all sorts of things in the game.

"I'm wary about what happened at Shrewsbury a few years ago. We went out then. And we got knocked out by Oldham as well.

"It's happened to us in the past that we've been knocked out, so of course we have to be wary. We have to try to make sure that doesn't happen, but we were trying to do that then as well, so there are no guarantees in football. You have to go and earn the right to win the games."